{"paper":{"title":"Thin Hessenberg Pairs and Double Vandermonde Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ali Godjali","submitted_at":"2011-07-27T02:25:38Z","abstract_excerpt":"A square matrix is called {\\it Hessenberg} whenever each entry below the subdiagonal is zero and each entry on the subdiagonal is nonzero. Let $V$ denote a nonzero finite-dimensional vector space over a field $\\fld$. We consider an ordered pair of linear transformations $A: V \\rightarrow V$ and $A^*: V \\rightarrow V$ which satisfy both (i), (ii) below.\n(i) There exists a basis for $V$ with respect to which the matrix representing $A$ is Hessenberg and the matrix representing $A^*$ is diagonal.\n(ii) There exists a basis for $V$ with respect to which the matrix representing $A$ is diagonal and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5369","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}